A295735 a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 0, a(1) = -1, a(2) = 0, a(3) = 1.

0, -1, 0, 1, 3, 8, 15, 31, 54, 101, 171, 304, 507, 875, 1446, 2449, 4023, 6728, 11007, 18247, 29766, 49037, 79827, 130912, 212787, 347795, 564678, 920665, 1493535, 2430584, 3940503, 6403855, 10377126, 16846517, 27289179, 44266768, 71687019, 116215931

Offset: 0

Author

Clark Kimberling, Nov 30 2017

Keywords

• easy
• sign

Comments

a(n)/a(n-1) -> (1 + sqrt(5))/2 = golden ratio (A001622), so that a( ) has the growth rate of the Fibonacci numbers (A000045).

Links

• Clark Kimberling, Table of n, a(n) for n = 0..2000
• Index entries for linear recurrences with constant coefficients, signature (1,3,-2,-2).

Crossrefs

Cf. A001622, A000045, A005672.

Programs

Mathematica

LinearRecurrence[{1, 3, -2, -2}, {0, -1, 0, 1}, 100]

Formula

a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 0; a(1) = -1, a(2) = 0, a(3) = 1.

G.f.: -3/(-1 + x + x^2) + (3 + 4*x)/(-1 + 2*x^2).